It's one of the first questions I ask when I'm building a character. What has this character's history given him in terms of fears and unresolved issues? And how are those going to shape his personality and his reactions to the events of the story? Because I like to make my main characters dig deep and work hard, that often means bringing them face to face with their mortal dreads. Whatever those might be.
Maybe that's part of why I like writing about men. In our society, it's perfectly okay for a woman to be afraid. But a man? Not so much. Or—maybe it's okay for him to be afraid, but he probably shouldn't admit it in company. Which means instead of giving in to his fears, he's got to either man up and face them, or he's got to find a way to avoid them.
Which is okay if he's afraid of alligators or hippopotami, or heights, which he can generally avoid if he needs to, with either a bit of slick talk or a well-timed case of the trots.
But what if he's afraid of something that's a lot harder to avoid? Or something he might have to confront in order to get what he wants? Like... commitment... or disapproval... or failure... or a pit filled with rabid ferrets?
That's when it gets fun.
Fears give me so much interesting stuff to play with (the visual here is the critter in the attic with the dull scissors and the purple construction paper, cutting out really horrific shapes to chuck into the story...). Whether he's trying to confront his fears or avoid them, fear can be used to manipulate him into a reaction that will serve the story, drive the plot, or build character.
Which probably has a lot to do with why I never get invited when the hot guys in my head decide to throw a party... even when I promise to make Death By Chocolate Brownies...